1 |
Z. Allen-Zhu and E. Hazan, Variance Reduction for Faster Non-Convex Optimization, Preprint arXiv:1603.05643, 2016.
|
2 |
Z. Allen-Zhu and Y. Li, LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain, Preprint arXiv:1607.03463v2, 2017.
|
3 |
Z. Allen-Zhu and Y. Yuan, Improved SVRG for Non-Strongly-Convex or Sum-of-NonConvex Objectives, Preprint arXiv:1506.01972v3, 2016.
|
4 |
J. Barzilai and J. M. Borwein, Two-point step size gradient methods, IMA J. Numer. Anal. 8 (1988), no. 1, 141-148.
DOI
|
5 |
L. Bottou, F. E. Curtis, and J. Nocedal, Optimization Methods for Large-Scale Machine Learning, Preprint arXiv:1606.04838v1, 2016.
|
6 |
J. P. Cunningham and Z. Ghahramani, Linear dimensionality reduction: survey, insights, and generalizations, J. Mach. Learn. Res. 16 (2015), 2859-2900.
|
7 |
D. Garber and E. Hazan, Fast and Simple PCA via Convex Optimization, Preprint arXiv:1509.05647v4, 2015.
|
8 |
G. H. Golub and C. F. Van Loan, Matrix Computations, fourth edition, Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, MD, 2013.
|
9 |
R. A. Horn and C. R. Johnson, Matrix Analysis, second edition, Cambridge University Press, Cambridge, 2013.
|
10 |
B. Jiang, C. Cui, and Y.-H. Dai, Unconstrained optimization models for computing several extreme eigenpairs of real symmetric matrices, Pac. J. Optim. 10 (2014), no. 1, 53-71.
|
11 |
S. J. Reddi, A. Hefny, S. Sra, and B. Poczos, Stochastic Variance Reduction for Nonconvex Optimization, Preprint arXiv:1603.06160v2, 2016.
|
12 |
R. Johnson and T. Zhang, Accelerating stochastic gradient descent using predictive variance reduction, Advances in Neural Information Processing Systems (2013), 315-323.
|
13 |
I. T. Jolliffe, Principal Component Analysis, second edition, Springer Series in Statistics, Springer-Verlag, New York, 2002.
|
14 |
H. Kasai, H. Sato, and B. Mishra, Riemannian stochastic variance reduced gradient on Grassmann manifold, Preprint arXiv:1605.07367v3, 2017.
|
15 |
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE, 86 (1998), no. 11, 2278-2324.
DOI
|
16 |
X. Liu, Z. Wen, and Y. Zhang, Limited memory block Krylov subspace optimization for computing dominant singular value decompositions, SIAM J. Sci. Comput. 35 (2013), no. 3, A1641-A1668.
DOI
|
17 |
Y. Saad, Numerical methods for large eigenvalue problems, revised edition of the 1992 original, Classics in Applied Mathematics, 66, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2011.
|
18 |
M. Schmidt, N. Le Roux, and F. Bach, Minimizing finite sums with the stochastic average gradient, Math. Program. 162 (2017), no. 1-2, Ser. A, 83-112.
DOI
|
19 |
S. Shalev-Shwartz and T. Zhang, Stochastic dual coordinate ascent methods for regularized loss minimization, J. Mach. Learn. Res. 14 (2013), 567-599.
|
20 |
O. Shamir, A Stochastic PCA and SVD Algorithm with an Exponential Convergence Rate, In The 32nd International Conference on Machine Learning (ICML 2015), 2015.
|
21 |
O. Shamir, Fast stochastic algorithms for SVD and PCA: convergence properties and convexity, Preprint arXiv:1507.08788v1, 2015.
|
22 |
J. H. Wilkinson, The Algebraic Eigenvalue Problem, Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York, 1988.
|
23 |
C. Tan, S. Ma, Y.-H. Dai, and Y. Qian, Barzilai-Borwein step size for stochastic gradient descent, Preprint arXiv:1605.04131v2, 2016.
|
24 |
D. S. Watkins, The Matrix Eigenvalue Problem, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007.
|
25 |
Z. Wen, C. Yang, X. Liu, and Y. Zhang, Trace-penalty minimization for large-scale eigenspace computation, J. Sci. Comput. 66 (2016), no. 3, 1175-1203.
DOI
|
26 |
Z. Xu and Y. Ke, Stochastic variance reduced Riemannian eigensolver, Preprint arXiv:1605.08233v2, 2016.
|
27 |
H. Zhang, S. J. Reddi, and S. Sra, Fast stochastic optimization on Riemannian manifolds, Preprint arXiv:1605.07147v2, 2017.
|